Question

A biochemical engineer has determined in her lab that the optimal productivity of a valuable antibiotic is achieved when the carbon nutrient, in this case molasses, is metered into the fermenter at a rate proportional to the growth rate. However, she cannot implement her discovery in the antibiotic plant, since there is no reliable way to measure the growth rate $(d X / d t)$ or biomass concentration $(X)$ during the course of the fermentation. It is suggested that an oxygen analyzer be installed on the plant fermenters so that the OUR (oxygen uptake rate, $\mathrm{g} / \mathrm{l}-\mathrm{h}$ ) may be measured. a. Derive expressions that may be used to estimate $X$ and $d X / d t$ from OUR and time data, assuming that a simple yield and maintenance model may be used to describe the rate of oxygen consumption by the culture. b. Calculate values for the yield $\left(Y_{\mathrm{X} \mathrm{O}_{2}}\right)$ and maintenance $\left(m_{\mathrm{O}_{2}}\right)$ parameters from the following data: $$ \begin{array}{rcc} \hline & \text { OUR } & X \\ \text { Time } & (\mathrm{g} / \mathrm{h}) & (\mathrm{g} / 1) \\ \hline 0 & 0.011 & 0.60 \\ 1 & 0.008 & 0.63 \\ 2 & 0.084 & 0.63 \\ 3 & 0.153 & 0.76 \\ 4 & 0.198 & 1.06 \\ 5 & 0.273 & 1.56 \\ 6 & 0.393 & 2.23 \\ 7 & 0.493 & 2.85 \\ 8 & 0.642 & 4.15 \\ 9 & 0.915 & 5.37 \\ 10 & 1.031 & 7.59 \\ 11 & 1.12 & 9.40 \\ 12 & 1.37 & 11.40 \\ 13 & 1.58 & 12.22 \\ 14 & 1.26 & 13.00 \\ 15 & 1.58 & 13.37 \\ 16 & 1.26 & 14.47 \\ 17 & 1.12 & 15.37 \\ 18 & 1.20 & 16.12 \\ 19 & 0.99 & 16.18 \\ 20 & 0.86 & 16.67 \\ 21 & 0.90 & 17.01 \\ \hline \end{array} $$ [Courtesy of D. Zabriskie from "Collected Coursework Problems in Biochemical Engineering," compiled by H. W. Blanch for $1977 \mathrm{Am}$. Soc. Eng. Educ. Summer School.] 

   A biochemical engineer has determined in her lab that the optimal productivity of a valuable antibiotic is achieved when the carbon nutrient, in this case molasses, is metered into the fermenter at a rate proportional to the growth rate. However, she cannot implement her discovery in the antibiotic plant, since there is no reliable way to measure the growth rate $(d X / d t)$ or biomass concentration $(X)$ during the course of the fermentation. It is suggested that an oxygen analyzer be installed on the plant fermenters so that the OUR (oxygen uptake rate, $\mathrm{g} / \mathrm{l}-\mathrm{h}$ ) may be measured.
a. Derive expressions that may be used to estimate $X$ and $d X / d t$ from OUR and time data, assuming that a simple yield and maintenance model may be used to describe the rate of oxygen consumption by the culture.
b. Calculate values for the yield $\left(Y_{\mathrm{X} \mathrm{O}_{2}}\right)$ and maintenance $\left(m_{\mathrm{O}_{2}}\right)$ parameters from the following data:
$$
\begin{array}{rcc}
\hline & \text { OUR } & X \\
\text { Time } & (\mathrm{g} / \mathrm{h}) & (\mathrm{g} / 1) \\
\hline 0 & 0.011 & 0.60 \\
1 & 0.008 & 0.63 \\
2 & 0.084 & 0.63 \\
3 & 0.153 & 0.76 \\
4 & 0.198 & 1.06 \\
5 & 0.273 & 1.56 \\
6 & 0.393 & 2.23 \\
7 & 0.493 & 2.85 \\
8 & 0.642 & 4.15 \\
9 & 0.915 & 5.37 \\
10 & 1.031 & 7.59 \\
11 & 1.12 & 9.40 \\
12 & 1.37 & 11.40 \\
13 & 1.58 & 12.22 \\
14 & 1.26 & 13.00 \\
15 & 1.58 & 13.37 \\
16 & 1.26 & 14.47 \\
17 & 1.12 & 15.37 \\
18 & 1.20 & 16.12 \\
19 & 0.99 & 16.18 \\
20 & 0.86 & 16.67 \\
21 & 0.90 & 17.01 \\
\hline
\end{array}
$$
[Courtesy of D. Zabriskie from "Collected Coursework Problems in Biochemical Engineering," compiled by H. W. Blanch for $1977 \mathrm{Am}$. Soc. Eng. Educ. Summer School.]
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Bioprocess Engineering
Bioprocess Engineering
Michael L Shuler 2nd Edition
Chapter 6, Problem 5 ↓
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A biochemical engineer has determined in her lab that the optimal productivity of a valuable antibiotic is achieved when the carbon nutrient, in this case molasses, is metered into the fermenter at a rate proportional to the growth rate. However, she cannot implement her discovery in the antibiotic plant, since there is no reliable way to measure the growth rate $(d X / d t)$ or biomass concentration $(X)$ during the course of the fermentation. It is suggested that an oxygen analyzer be installed on the plant fermenters so that the OUR (oxygen uptake rate, $\mathrm{g} / \mathrm{l}-\mathrm{h}$ ) may be measured. a. Derive expressions that may be used to estimate $X$ and $d X / d t$ from OUR and time data, assuming that a simple yield and maintenance model may be used to describe the rate of oxygen consumption by the culture. b. Calculate values for the yield $\left(Y_{\mathrm{X} \mathrm{O}_{2}}\right)$ and maintenance $\left(m_{\mathrm{O}_{2}}\right)$ parameters from the following data: $$ \begin{array}{rcc} \hline & \text { OUR } & X \\ \text { Time } & (\mathrm{g} / \mathrm{h}) & (\mathrm{g} / 1) \\ \hline 0 & 0.011 & 0.60 \\ 1 & 0.008 & 0.63 \\ 2 & 0.084 & 0.63 \\ 3 & 0.153 & 0.76 \\ 4 & 0.198 & 1.06 \\ 5 & 0.273 & 1.56 \\ 6 & 0.393 & 2.23 \\ 7 & 0.493 & 2.85 \\ 8 & 0.642 & 4.15 \\ 9 & 0.915 & 5.37 \\ 10 & 1.031 & 7.59 \\ 11 & 1.12 & 9.40 \\ 12 & 1.37 & 11.40 \\ 13 & 1.58 & 12.22 \\ 14 & 1.26 & 13.00 \\ 15 & 1.58 & 13.37 \\ 16 & 1.26 & 14.47 \\ 17 & 1.12 & 15.37 \\ 18 & 1.20 & 16.12 \\ 19 & 0.99 & 16.18 \\ 20 & 0.86 & 16.67 \\ 21 & 0.90 & 17.01 \\ \hline \end{array} $$ [Courtesy of D. Zabriskie from "Collected Coursework Problems in Biochemical Engineering," compiled by H. W. Blanch for $1977 \mathrm{Am}$. Soc. Eng. Educ. Summer School.]
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Key Concepts

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Parameter Estimation Using Experimental Data
Estimating the yield and maintenance parameters from experimental data involves analyzing time-series measurements of oxygen uptake and biomass concentration. By manipulating the yield and maintenance model, one can correlate the measured OUR with the rate of biomass growth (dX/dt) and the current biomass concentration (X). Techniques such as differential calculus or regression analysis are used to deduce these parameters from experimental trends, enabling process optimization and better control over the fermentation process.
Maintenance Coefficient
The maintenance coefficient accounts for the oxygen consumed by cells for functions other than growth, such as sustaining cellular integrity and basic metabolic activities. Even when the cells are not actively proliferating, they require energy to maintain vital processes. This parameter helps differentiate between oxygen consumption used for growth and that for maintenance, thereby enabling a more accurate assessment of the process performance.
Yield and Maintenance Model
The yield and maintenance model is a mathematical formulation that relates the oxygen uptake rate to both biomass production and cellular maintenance. In this model, oxygen consumption is partitioned into a fraction used for synthesizing new cell mass (governed by the yield coefficient) and a fraction that accounts for cellular maintenance (characterized by the maintenance coefficient). The typical form of the model is expressed as OUR = (1/Y_x/O2)(dX/dt) + m_O2 * X, which provides a framework to estimate both biomass concentration and its growth rate from oxygen consumption data.
Oxygen Uptake Rate (OUR)
The Oxygen Uptake Rate (OUR) is a quantitative measure of how much oxygen is consumed per unit time and per unit volume in a bioprocess. It is an important online monitoring parameter that indirectly reflects the metabolic activity and growth intensity of the culture. In typical bioprocesses, OUR is used to infer cellular activity and can be linked to biomass formation through appropriate models, making it a critical variable when direct biomass measurements are impractical.
Yield Coefficient
The yield coefficient in biochemical processes describes the efficiency of converting a substrate (or in this context, oxygen) into biomass. Specifically, it relates the amount of oxygen consumed to the amount of new cell mass produced during the growth process. This parameter is essential for understanding and predicting the productivity of the fermentation process, as it quantifies the efficiency of the conversion process.
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Transcript

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0:00 E.
00:01 Coli, ethanol, tolerant.
00:22 Ethanol is one of the mixed acid fermentation.
00:31 Mixed acid fermentation and produce of e.
00:42 Coli.
00:46 And products of e .culi, its production in wild type cells of e .culi is catalyzed in a two -step reaction.
01:13 In two -step reaction by alcohol, dehydrogenase...
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